Standard syllabus
Finite element methods · Graduate · Math
Topics
Variational foundations
- Weak formulations of elliptic boundary-value problems
- Lax–Milgram theorem and well-posedness
- Galerkin and Petrov–Galerkin approximations
- Energy norms and best approximation in Hilbert spaces
- Abstract error estimates (Céa's lemma)
Finite element spaces
- Piecewise polynomial elements on triangulations and meshes
- Reference elements, shape functions, and assembly
- Interpolation error and approximation theory
- h-refinement vs p-refinement (introduction)
- Mixed finite elements (introduction)
Time-dependent and hyperbolic problems
- Method of lines for parabolic problems
- Stability of time discretizations (theta methods overview)
- A posteriori error estimation (introduction)
- Adaptive mesh refinement driven by error indicators
- Introduction to discontinuous Galerkin methods
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